Beijing - Hong Kong - Shanghai is it possible with 144 hour visa

Yes, this is fine, but you have to have in mind that the immediate airport before your arrival in Beijing cannot be Hong Kong. In other words, your itinerary should look like this, for example:

Seoul - Beijing - Hong Kong - Shanghai - Seoul

In other words, the immediate points before and after your mainland Chinese destination have to be in two different countries or eligible territories (eligible territories: Hong Kong, Taiwan and Macau).

By the way, I encourage you to use correct terminology because it is not 144 hour visa, but 144 hour visa free transit since there is no visa of any kind.